This section provides background information related to the present disclosure which is not necessarily prior art.
In recent years, the multiple input multiple output (MIMO) technology has become a major concern and has been applied in actual communication systems, owing to its ability of improving the transmit spectral efficiency and the reliability of wireless communication systems. In addition, the multi-carrier orthogonal frequency division multiplexing (OFDM) technology has become the focus of study, owing to its ability of overcoming the multipath considerations of wireless channels and achieving a higher spectral efficiency than single-carrier systems. MIMO and OFDM become the key technologies of mobile communication systems and have been widely applied in approaches including long term evolution (LTE) of third generation (3G) mobile communication systems and even fourth generation (4G) mobile communications systems.
Various transmit diversity and spatial multiplexing approaches can be implemented based on MIMO and OFDM technologies. Diversity gain can improve the performance of systems, and spatial multiplexing gain can improve the transmission rate.
A spatial-frequency encoding approach of the prior art, which is an extension of space-time encoding, replaces the time dimension of space-time encoding with frequency dimension for encoding. This approach is applied mainly in OFDM systems. As shown in FIG. 1, spatial-frequency encoding can obtain diversity gain or spatial multiplexing gain by encoding on multiple sub-carriers and antennas. At present, spatial-frequency encoding is categorized into space frequency block code (SFBC) and spatial multiplexing coding. When the encoding rate of SFBC is equal to or lower than 1, the transmitter performs orthogonal or non-orthogonal encoding on multiple antennas, and the receiver performs maximum likelihood decoding to obtain diversity gain. At present, 2-antenna transmitting based on orthogonal spatial-frequency encoding is applied most widely. Formula (1) shows the encoding matrix.
                    G        =                  (                                                                      S                  1                                                                              -                                      S                    2                    *                                                                                                                        S                  2                                                                              S                  1                  *                                                              )                                    (        1        )            
In formula (1), S1 and S2 are the symbols before spatial-frequency encoding. After 2-antenna transmitting based on orthogonal spatial-frequency encoding indicated by formula (1), transmit antenna 1 transmits S1 on the sub-carrier k and −S2* on the sub-carrier k+1; transmit antenna 2 transmits S2 on the sub-carrier k and S1* on the sub-carrier k+1. It is defined that the encoding rate is n/k, where n indicates the number of data symbols transmitted during one spatial-frequency encoding operation, and k indicates the number of the sub-carriers required for one spatial-frequency encoding operation. As seen from formula 1, the encoding rate for 2-antenna transmitting based on orthogonal spatial-frequency encoding is (1). The multiple sub-carriers occupied for one spatial-frequency encoding operation are hereinafter called a sub-carrier set.
It is supposed that the receiver has only one receive antenna, and that the channel fading factors for the data on two adjacent sub-carriers of the same transmit antenna are the same. The data received by the antenna on two sub-carriers can be expressed by formulas (2) and (3).r1=h1S1+h2S2+n1  (2)r2=h1(−S2*)+h2S1*+n2  (3)
h1 and h2 indicate the factors for channel fading from the two transmit antennas to the receive antenna. After channel estimation, the receiver can perform the maximum likelihood decoding, as expressed by formulas (4) and (5).Ŝ1=h1*r1+h2r2*=(|h1|2+|h2|2)S1+h1*n1+h2n2*  (4)Ŝ2=h2*r1−h1r2*=(|h1|2+|h2|2)S2−h1n2*+h2*n1  (5)
Ŝ1 and Ŝ2 indicate the estimation of the symbols S1 and S2.
As seen from formulas (4) and (5), S1 and S2 each obtain second-order diversity after they are transmitted through the STBC transmit diversity.
When the number of transmit antennas is 3 or 4, only the orthogonal spatial-frequency encoding at rates of ½ and ¾ exists.
Formula (6) shows the matrix of 3-antenna transmitting based on orthogonal spatial-frequency encoding at a rate of ½:
                              G                      3            ,            1                          =                              (                                                                                S                    1                                                                                        S                    2                                                                                        S                    3                                                                                                                    -                                          S                      2                                                                                                            S                    1                                                                                        -                                          S                      4                                                                                                                                        -                                          S                      3                                                                                                            S                    4                                                                                        S                    1                                                                                                                    -                                          S                      4                                                                                                            -                                          S                      3                                                                                                            S                    2                                                                                                                    S                    1                    *                                                                                        S                    2                    *                                                                                        S                    3                    *                                                                                                                    -                                          S                      2                      *                                                                                                            S                    1                    *                                                                                        -                                          S                      4                      *                                                                                                                                        -                                          S                      3                      *                                                                                                            S                    4                    *                                                                                        S                    1                    *                                                                                                                    -                                          S                      4                      *                                                                                                            -                                          S                      3                      *                                                                                                            S                    2                    *                                                                        )                    T                                    (        6        )            
Formula (7) shows the matrix of 4-antenna transmitting based on orthogonal spatial-frequency encoding at a rate of ½:
                              G                      4            ,            1                          =                              (                                                                                S                    1                                                                                        S                    2                                                                                        S                    3                                                                                        S                    4                                                                                                                    -                                          S                      2                                                                                                            S                    1                                                                                        -                                          S                      4                                                                                                            S                    3                                                                                                                    -                                          S                      3                                                                                                            S                    4                                                                                        S                    1                                                                                        -                                          S                      2                                                                                                                                        -                                          S                      4                                                                                                            -                                          S                      3                                                                                                            S                    2                                                                                        S                    1                                                                                                                    S                    1                    *                                                                                        S                    2                    *                                                                                        S                    3                    *                                                                                        S                    4                    *                                                                                                                    -                                          S                      2                      *                                                                                                            S                    1                    *                                                                                        -                                          S                      4                      *                                                                                                            S                    3                    *                                                                                                                    -                                          S                      3                      *                                                                                                            S                    4                    *                                                                                        S                    1                    *                                                                                        -                                          S                      2                      *                                                                                                                                        -                                          S                      4                      *                                                                                                            -                                          S                      3                      *                                                                                                            S                    2                    *                                                                                        S                    1                    *                                                                        )                    T                                    (        7        )            
Formula (8) shows the matrix of 3-antenna transmitting based on orthogonal spatial-frequency encoding at a rate of ¾:
                              G                      3            ,            2                          =                              (                                                                                S                    1                                                                                        -                                          S                      2                                                                                                            -                                          S                      3                                                                                                                                        S                    2                    *                                                                                        S                    1                    *                                                                    0                                                                                                  S                    3                    *                                                                    0                                                                      S                    1                    *                                                                                                0                                                                      -                                          S                      3                      *                                                                                                            S                    2                    *                                                                        )                    T                                    (        8        )            
Formula (9) shows the matrix of 4-antenna transmitting based on orthogonal spatial-frequency encoding at a rate of ¾:
                              G                      4            ,            2                          =                              (                                                                                S                    1                                                                                        S                    2                                                                                        S                    3                                                                    0                                                                                                  -                                          S                      2                      *                                                                                                            S                    1                    *                                                                    0                                                                      -                                          S                      3                                                                                                                                        -                                          S                      3                      *                                                                                        0                                                                      S                    1                    *                                                                                        S                    2                                                                                                0                                                                      S                    3                    *                                                                                        -                                          S                      2                      *                                                                                                            S                    1                                                                        )                    T                                    (        9        )            
When the encoding rate of spatial multiplexing coding is higher than 1, different data is transmitted on the same sub-carrier of different antennas to improve the data transmission rate, that is, to obtain spatial multiplexing gain. Formulas (10) to (12) show the matrixes of spatial multiplexing coding when the number of transmit antennas is 2, 3, and 4.
                              G          2                =                              (                                                                                S                    1                                                                                                                    S                    2                                                                        )                    ⁢                                          ⁢          —Sending          ⁢                                                            ⁢                                                          ⁢          two          ⁢                                          ⁢          data          ⁢                                          ⁢          streams          ⁢                                          ⁢          at          ⁢                                          ⁢          the          ⁢                                          ⁢          same          ⁢                                          ⁢          time                                    (        10        )                                          G          3                =                              (                                                                                S                    1                                                                                                                    S                    2                                                                                                                    S                    3                                                                        )                    ⁢                                          ⁢          —Sending          ⁢                                          ⁢          three          ⁢                                          ⁢          data          ⁢                                          ⁢          streams          ⁢                                          ⁢          at          ⁢                                          ⁢          the          ⁢                                          ⁢          same          ⁢                                          ⁢          time                                    (        11        )                                          G          4                =                              (                                                                                S                    1                                                                                                                    S                    2                                                                                                                    S                    3                                                                                                                    S                    4                                                                        )                    ⁢                                          ⁢          —Sending          ⁢                                                            ⁢                                                          ⁢          four          ⁢                                          ⁢          data          ⁢                                          ⁢          streams          ⁢                                          ⁢          at          ⁢                                          ⁢          the          ⁢                                          ⁢          same          ⁢                                          ⁢          time                                    (        12        )            
According to the definition of encoding rate, the encoding rates in formula (10), formula (11), and formula 12 are 2, 3, and 4 respectively. Compared with SFBC at a rate of 1, spatial multiplexing coding improves the data transmission rate dramatically.
Therefore, when only SFBC of the prior art is used, spatial multiplexing gain cannot be obtained, and the transmission rate of the system is decreased because the encoding rate of SFBC is lower than 1 when the number of transmit antennas is greater than 2. Alternatively, when only spatial multiplexing coding of the prior art is used, though spatial multiplexing gain can be obtained by concurrent transmission of multiple data streams, each data stream cannot obtain diversity gain, and the transmission reliability of each data stream is decreased.
Cyclic shift diversity (CSD) of the prior art is also a transmit diversity technology applied in OFDM systems. In this solution, frequency diversity gain is obtained in a way that the same OFDM symbols are cyclically shifted in different modes in the time domain and then transmitted by different antennas. FIG. 2 shows the structure of the transmitter.
If a system has M transmit antennas, the OFDM symbols after IFFT processing are respectively input to M transmit antennas. The OFDM symbols on the first antenna are not shifted cyclically (cyclic shift=0), and those on the other antennas are shifted cyclically with different shift bits (δm, m=1, 2, . . . M, where δ1=0). Supposing that the length of IFFT is N, the number of cyclic shift bits must meet the following condition: 0≦δm≦N−1. After cyclic shift, a cyclic prefix must be added to the OFDM symbols on each antenna before the symbols are transmitted by different antennas at the same time.
In fact, the OFDM symbols transmitted on different antennas are only different cyclic shifts of the same OFDM symbol in the time domain. It is supposed that the signal of the OFDM symbol in the time domain is x(n), (0≦n≦N−1), and that the signal corresponding to each sub-carrier in the frequency domain is X(k), k=0, . . . N−1. Because the CP lengths are the same, the orthogonality of sub-carriers does not change. As seen from FFT, cyclic shifts in the time domain are equivalent to the symbols in the frequency domain plus a phase rotation. Then, the signal obtained after the rotation is as follows:Z(k)=X(k)e−j2πδ/N,k=0, . . . N−1  (13)
In formula (13), δ indicates the number of cyclic shift bits in the time domain. According to the preceding relations of shift bits, the signal on each sub-carrier of each antenna in the frequency domain can be obtained:Zm(k)=X(k)e−j2πδm/N,k=0, . . . N−1;m=1, . . . M  (14)
Supposing that the number of the receive antennas on the receiver is 1, the signal received by the receiver in the frequency domain is as follows:
                                                                                          Y                  ⁡                                      (                    k                    )                                                  =                                                                            ∑                                              m                        =                        1                                            M                                        ⁢                                                                                  ⁢                                                                                            H                          m                                                ⁡                                                  (                          k                          )                                                                    ⁢                                                                        Z                          m                                                ⁡                                                  (                          k                          )                                                                                                      +                                      N                    ⁡                                          (                      k                      )                                                                                                                                                                =                                                                                    X                        ⁡                                                  (                          k                          )                                                                    ⁢                                                                        ∑                                                      m                            =                            1                                                    M                                                ⁢                                                                                                  ⁢                                                                                                            H                              m                                                        ⁡                                                          (                              k                              )                                                                                ⁢                                                      ⅇ                                                                                          -                                j2π                                                            ⁢                                                                                                                          ⁢                              k                              ⁢                                                                                                                          ⁢                                                                                                δ                                  m                                                                /                                N                                                                                                                                                                          +                                          N                      ⁡                                              (                        k                        )                                                                                            ,                                                    ⁢                                  ⁢                              k            =            0                    ,                                    …              ⁢                                                          ⁢              N                        -            1                                              (        15        )            
Y(k) indicates the signal received on sub-carrier k. Hm(k) indicates the response from the frequency domain channel between transmit antenna m and the receive antenna on sub-carrier k. N(k) indicates additive white Gaussian noise (AWGN).
According to the result of formula (15), the multi-antenna system can be equivalent to a single-antenna system:Y(k)=He(k)X(k)+N(k),k=0, . . . N−1  (16)
The equivalent channel is as follows:
                                          H            e                    ⁡                      (            k            )                          =                              ∑                          m              =              1                        M                    ⁢                                          ⁢                                                    H                m                            ⁡                              (                k                )                                      ⁢                          ⅇ                                                -                  j2π                                ⁢                                                                  ⁢                k                ⁢                                                                  ⁢                                                      δ                    m                                    /                  N                                                                                        (        17        )            
According to the final equivalent results, cyclic shift of different antennas in the time domain is equivalent to introduction of multipath in the time domain, which enhances frequency selection in the frequency domain. In this way, frequency diversity gain can be obtained through channel coding before OFDM modulation. In comparison with a single-antenna system, this cyclic shift method helps to obtain greater frequency diversity gain under the same channel coding and interleaving.
For details about CSD, refer to the Multicarrier Delay Diversity Modulation for MIMO Systems. 
When used alone to implement diversity, however, OFDM-based CSD has some inevitable defects: (i) the frequency diversity gain can be obtained only through channel coding; (ii) though CSD ensures that the encoding rate is 1, full-diversity gain is unavailable, and the diversity performance is inferior to orthogonal SFBC; (iii) improper delay values may lead to no frequency response on some sub-carriers, cause a puncturing effect, and affect the performance of decoders; and (iv) using CSD and SFBC together changes the responses of channels in the frequency domain, thus affecting the orthogonality of SFBC and decreasing the performance of SFBC.